Nonlinear strategies for longitudinal control in the stabilization of an oscillating suspended cable

The feasibility of reducing vibrations in suspended cables by an imposed longitudinal displacement of one support is investigated through an analytical model. A noncollocated active control scheme is considered where modal amplitudes describing transverse oscillations are used in the feedback control action at the boundary. A 2DOF nonlinear model of the cable is used to design state-feedback controller. Linear and nonlinear velocity feedback and feedback bilinearisation are shown to produce a nonlinear and bilinear actively-damped system, respectively. The controlled system performance is analysed comparing the effectiveness of the different strategies on both control demand and response amplitudes in the stabilization of the equilibrium position. Control spillover effects are commented through an enlarged 8DOF modal description of the controlled cable oscillations.